Primarily a problem at low Galactic latitudes, since dust concentrated to plane of the
Galaxy.

The edge-on galaxy NGC 891 showing prominent dust layer, similar to what we expect
in the Milky Way. Note filamentary structure.
From http://antwrp.gsfc.nasa.gov/apod/ap020703.html.

In Milky Way, creates a Zone of Avoidance for studies of the far Galaxy and
extragalactic sources.
Before discovery, gave a very confusing picture of the Milky Way structure.

Herschel's universe (Milky Way) made from starcounts. The pinching in
on the right is due to a loss of stars due to reddening.

At low Galactic latitudes the reddening can be very clumpy.

Examples of Galactic dark clouds: The famous horsehead and coalsack dark nebulae.

A new view of the dust distribution near the Galactic plane by UVa grad student
David Nidever & SRM. The fine scale filigree in the dust distribution is obvious.

Dark Clouds:

These are seen as silhouettes blocking light from sources behind
them.

The background sources may be stars, as in the case of the
so-called "Coal-sack" (the Australian aboriginal "Eagle's Nest").

The background source may be a bright nebula, as in the case
of the "horsehead nebula".

Very compact, dark clouds that are likely places of
star formation in the (astronomically) near future are known
as Bok globules.

Bok globules in front of glowing IC 2944 cloud.

But wispy dust clouds even exist at high latitudes: Infrared Cirrus

IRAS cirrus.

Infrared cirrus around the Magellanic Clouds
as seen in the extinction maps of Schlegel, Finkbeiner & Davis
(1998, ApJ, 500, 525) from the COBE far infrared emission maps.
Image by David Nidever (UVa).

Therefore, absorption in magnitudes is numerically equivalent to optical depth along
line of sight.
Since N(x) is a constant to any star, and Aλ = 1.086 τλ = k λ N(x), any variation in Aλ reflects k λ.

Aλ is larger in the UV and smaller in the IR.

The variation of Aλ with
λ actually allows us to detect its presence and measure it.

If we adopt a crude model of distribution of n(x) as a homogeneous slab
(a representative thickness would be ±150 pc),
then we have a cosecant law for the extinction as follows:

Then

cos(90o-b) = τ1 / τ(b)
sin b = τ1 / τ(b)
τ(b) = τ1 csc b

and we have from before that:

A(b)λ = 1.086 τλ = 1.086 τ1 csc b
= Aλ(90o) + 1.086 τ1 (cscb - 1)

with

Aλ(90o) < ~0.05
Aλ(0o) ---> ∞ ("Zone of Avoidance").

In reality, as shown above, the extinction is very patchy (not like a slab).

The above technique is harder when you are inside slab, because it
is hard to isolate only
extinction in front of star.

Interstellar Reddening in the UBV System
ISM dust makes objects redder (like Sun and Moon on horizon
on hazy, dusty, polluted days).
Recall λ-1 dependence from Mie scattering
(scattering radius large compared to wavelength) --
found by Trumpler -- allows us to determine net interstellar absorption:
A(λi ), which is defined
by the amount of absorption in magnitudes at λi :

PAHs or fragments of graphite sheets onto which H or other atoms adhere.

In Binney & Merrifield, Figure 3.17, the log of both axes of the above plot is shown (to stress the
IR part of the extinction curve).

Note that the book has incorrectly labeled the axes of this plot.

Note λ-1 dependence for much of optical-IR
region.

The 9.7 and 18 micron features are probably associated with Si-O bonds
in silicate grains.

Note how much less extinction there is at long wavelengths.
For example, AK/AV is about 10%.
--> clearly observations in the IR are best for studying dusty objects.

Visible (left) and Near-Infrared View of the Galactic Center
Visible image courtesy of Howard McCallon. The infrared image is
from the
2 Micron All Sky Survey (2MASS). Images and caption from
http://www.ipac.caltech.edu/Outreach/Edu/Regions/irregions.html.

Cluster Method for Determining RV

For any cluster, (V -
MV )0 = constant

For a reddened cluster, variations in (V - MV)
are produced by variations in the amount of reddening along line of sight to individual
stars.

Thus, for reddened cluster, each star shows:

V - MV = C + AV

where C is constant for the whole cluster (depending on only the distance of
the cluster), and AV
depends on the relative total absorption in front of each star, which varies. Then:

V - MV = C + AV
= C + RV E(B-V)

To find RV , determine the MK types and UBV
mags of different cluster stars.

The MK types give MV and
(B-V)0 .

Then plot (V - MV ) versus
E(B-V) for all stars in cluster:

which gives RV from slope.

Most clusters give RV ~ 3.1.
This is the standard value of diffuse ISM.

Variations in RV

RV ~ 3.1 in most regions of the sky.

But anomalous RV found, especially in
cores of dense clouds.

THE BAD NEWS: Find RV varies across
2.7 RV

Plot from Cardelli et al. (1989, ApJ, 345, 245).

THE GOOD NEWS: Cardelli, Clayton, & Mathis (1989, ApJ, 345, 245)
showed that there is a universal mean extinction law that does indeed only
scale with a single parameter, for which they adopt RV

That is, the variation of Aλ / AV follows a
linear dependence with RV-1,
e.g.,:

The above plots show that there is a linear relationship between
Aλ / AV at
about all wavelengths that only depends on one parameter, selected as
RV . This means that the entire
Aλ curve scales in shape with
RV . From Cardelli et al. (1989).

.

Thus, there is a universal shape to the extinction law that only
depends on RV (the slope at V, but any similar
scaling variable could be picked).

Plot from Cardelli et al. (1989, ApJ, 345, 245).

Why is the universal shape so unexpected?

The Aλi curve
presumable reflects:

grain sizes

grain composition

Recall:

where the k are cross-sections.

The ISM is a complicated place with many processes going on.

Even lines of sight with same RV might be expected to have
different physical conditions that would selectively modify a particular
component, grain type, or grain size selectively over others.

But the actual ISM seems to modify the entire extinction law
in a regular and continuous way, i.e. effectively working on all grain
sizes and types continuously and efficiently (e.g., through shocks,
spallation, and/or scattering.)

For once, Nature is kind.

Dust-to-Gas Ratio

A related way in which Nature is somewhat kind -- E(B-V) is found
to be directly proportional to the column density of Hydrogen in all
its forms (H, H2, H+):

Measuring Reddening to (Hot) Gaseous Sources

But also show emission lines in H series (Lyman, Balmer, Paschen) --
normally ionized HII gas would not show these transitions.

These "optical recombination lines" are caused by captured electrons
cascading down to ground state

In limit of low density, only see downward transitions (and then
reionization)

Relative intensities of lines are only weakly dependent on
temperature and not on density (as long as low density) and can be
easily calculated by a "cascade matrix" of transition probabilities
for a given photoionization rate

Case A recombination theory - all line photons emitted from nebula
escape without absorption - such low optical depth regions are hard to
see

Case B recombination theory - more typical optical depths large for
Lyman resonance lines and line photons bounce around / scatter many
times before transition downward.

So Case B more widely used, better (Lyman photons scatter many times
before converting to lower series). Somewhere between case A and B is
correct

Extinction Maps
Several ways to map the extinction with position in the galaxy.

Assume simple law with Galactic latitude:

For example, simple slab and "cosecant law" (with width ±150 pc):

Galaxy counts:

Hubble realized that the variation in counts of faint galaxies could be
explained by dust extinction.
Assume mean count-magnitude relation.
Deviations from that law are directly related to total column
density of dust.
For homogeneously populated universe in the absence of dust, the number
of galaxies as a function of magnitude, mo, is:

log N(m) = 0.6mo + c

(You should prove this to yourself.)
A galaxy at b that should be
at a magnitude mo without dust will appear at a
fainter magnitude of

m(b) = mo + Aλ(b).
mo = m(b) - Aλ(b).

Thus, in the presence of dust, we will get fewer galaxies at a given magnitude:

log N(m,b) = log No(m) - 0.6 Aλ

Famous maps made with this method are those of Burstein & Heiles (1983).